What happens when beta is near zero or negative?

The ratio stops being usable. A beta approaching zero sends the score towards infinity, so a market-neutral strategy scores spectacularly on an arithmetic accident rather than on merit. A negative beta flips the sign, and a positive excess return then produces a negative Treynor, which ranks below a portfolio that lost money. Neither result is a judgement about the strategy — both are the division misbehaving near a denominator it was never meant to approach. Wherever beta is small, unstable or negative, use a measure whose denominator cannot vanish.

Which risk-free rate should go in?

One denominated in the same currency as the portfolio and covering the same horizon as the returns being measured. A euro portfolio measured against a dollar rate imports an exchange-rate assumption nobody stated, and an annual return compared to an overnight rate mismatches the horizon. The choice matters more than it used to: when cash paid nothing the subtraction barely moved the numerator, and at 4.5 per cent it removes more than a third of a 12.5 per cent return. Whatever you pick, use the same series for every portfolio you compare, or the comparison measures your rate choices rather than their performance.

The Treynor Ratio Is Only as Solid as Its Beta

Published 10/14/2026 · 3 min read · Finance calculators

Camille Laurent — Finance writer at OneKitly

Tax · Personal finance

Checked against 2 sources

View profile →

In short

The Treynor ratio takes the return above the risk-free rate and divides it by beta: a portfolio returning 12.5 per cent while cash pays 4.5 has 8 points of excess return, and at a beta of 1.2 that scores 6.67. The reward part of the fraction is measured; the risk part is not. Beta comes from regressing the portfolio's returns against an index over a chosen window, and both choices move it. Re-estimate the same portfolio at a beta of 0.6 and the score doubles to 13.33 without a single position changing. A ranking built on Treynor is therefore a ranking of return estimates divided by regression outputs, and it deserves the same scepticism you would apply to any figure whose denominator has a confidence interval nobody prints.

Eight points of excess return over a beta of 1.2 gives 6.67. Change the beta to 0.6 and the same portfolio scores 13.33 — the number moves entirely on an estimate.

A plausible estimation error is worth forty per cent

Betas quoted to two decimals routinely carry a standard error of a tenth or two, and a range of 1.0 to 1.4 around a central 1.2 is not an unusual one. Across that range the Treynor score runs from 8.00 down to 5.71 — the top of the interval is forty per cent above the bottom, with nothing in the portfolio having changed. Two funds separated by less than that in a league table are not distinguishable by this measure, and treating the ranking as fine-grained reads noise as skill. The honest use is to sort into broad bands and to ask what else differs between the candidates.

It answers a narrower question than it looks

Beta measures only the part of a portfolio's movement that tracks the market, so the ratio charges nothing for risk that diversification could remove. That is the right choice when the portfolio is one sleeve inside a larger diversified whole, where its idiosyncratic wobbles genuinely wash out against everything else. It is the wrong choice when the portfolio is somebody's entire savings, because there the wobbles do not wash out and the measure that divides by total volatility answers the actual question. Same numerator, different denominator, different question — and a fund concentrated in a handful of names can look excellent on one and mediocre on the other for entirely sound reasons.

Treynor

12.5 % return, 4.5 % risk-free — the score against beta
Beta	Excess return	Treynor
0.6	8 pts	13.33
1.0	8 pts	8.00
1.2	8 pts	6.67
1.4	8 pts	5.71

Worked with our own calculator

Treynor ratio calculator

Given

Portfolio return (Rp): 11.25%
Risk-free rate (Rf): 4.05%
Portfolio beta (β): 0.6
Portfolio σ (optional, for Sharpe): 1%

Result

Treynor ratio (pp): 12
Excess return: 7.2%
Sharpe ratio (if σ given): 7.2

These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.

Run it on your own figures →

Frequently asked questions

What happens when beta is near zero or negative?: The ratio stops being usable. A beta approaching zero sends the score towards infinity, so a market-neutral strategy scores spectacularly on an arithmetic accident rather than on merit. A negative beta flips the sign, and a positive excess return then produces a negative Treynor, which ranks below a portfolio that lost money. Neither result is a judgement about the strategy — both are the division misbehaving near a denominator it was never meant to approach. Wherever beta is small, unstable or negative, use a measure whose denominator cannot vanish.
Which risk-free rate should go in?: One denominated in the same currency as the portfolio and covering the same horizon as the returns being measured. A euro portfolio measured against a dollar rate imports an exchange-rate assumption nobody stated, and an annual return compared to an overnight rate mismatches the horizon. The choice matters more than it used to: when cash paid nothing the subtraction barely moved the numerator, and at 4.5 per cent it removes more than a third of a 12.5 per cent return. Whatever you pick, use the same series for every portfolio you compare, or the comparison measures your rate choices rather than their performance.

Articles you may find interesting

All guides →

ExplainerThe Sharpe Ratio, and What It Quietly AssumesSharpe = (return − risk-free) ÷ standard deviation, so it prices return per unit of volatility — and volatility is symmetric. Two funds can share a Sharpe of 0.4939 while their Sortino ratios are 8.59 and 0.74. Annualising by √12 assumes independent returns: at an autocorrelation of 0.2 the published figure is 20 percent too high.ExplainerThe Sortino Denominator Nobody Agrees OnOn one twelve-month series the Sortino ratio is 7.7518 or 3.8759 depending only on whether the squared shortfalls are divided by all twelve months or by the three below target. The two conventions differ by exactly the square root of twelve over three, and they can rank two funds in opposite orders.ExplainerVolatility Is Not Risk, and the Square Root of Time Is a ChoiceAnnualised volatility = period standard deviation × √(periods per year), and that √t scaling assumes independent increments. It is a model, not arithmetic: at a daily autocorrelation of 0.1 a 60 percent annualised figure should read 66.3. The payload is volatility drag — the arithmetic mean exceeds the geometric by about σ²/2, so at 8 percent average return and 40 percent volatility the compound outcome is zero.ExplainerRisk/Reward Ratio Explained: The Win Rate Each Ratio RequiresA 1:3 ratio does not make you right more often — it lets you be wrong three times out of four and still break even. Here is the inversion, a table of ratio against required win rate, and what costs do to both.ExplainerTwo Accepted Models, Two Points Apart on the Same CompanyCAPM and the dividend growth model both compute the cost of equity. On one set of inputs they give 9 % and 7 % — and the choice between them decides a valuation more than any figure inside either.GuideWhere to Set a Stop-Loss and a Take-ProfitThe stop goes where your idea is wrong, not where your comfort runs out — and then the position size adapts to it. Here is the volatility argument, the sizing arithmetic, and the win rate each reward multiple demands.

Sources

Spotted a mistake in this article?